Hi Lisa, welcome to the forums......
I tend to agree with Mike17, though it's not easy to suggest a paint without knowing where you might be.....a brand available in the U.S. may not be available in Canada or the UK, OZ or NZ.....
Also, not knowing what size cage you're considering might affect the type of spray paint that would be appropriate.....most spray paints are termed enamel, epoxy and acrylic and each has properties suitable for different applications.....
With the exception of acrylics, often referred to as water based paint, enamels & epoxies contain solvents which can affect the paint already on the cage.....a test spraying is usually recommended, in an area not readily visible.....
Small cages, budgie & 'tiel sized, are normally coated with enamel type paints, larger cages with square and/or round tubing construction are normally power coated.....no cages are acrylic coated with water based paints, except maybe in an aftermarket setting.....
If you are in the U.S. people have found Krylon brand paints to be suitable for repainting of bird cages, though to insure proper curing, you might want to wait 2 weeks to 28 days, paints take up to 28 days to properly cure, even when they may feel dry in 2-8 hours after application.....
Prior to painting, you will want to carefully wipe the cage down with alcohol, to remove any oils and/or release agents, so your new paint will adhere properly.....
Good luck.....